Gödel makes a rather strong comparison between "the question of theobjective existence of the objects of mathematical intuition" and the"question of the objective existence of the outer world" which heconsiders to be "an exact replica."

Gödel's rejection of Russell's "logical fictions" may be seen as arefusal to regard mathematical objects as "insignificant chimeras ofthe brain."

Gödel's realism, although similar to that of Locke and Leibniz, placesemphasis on the fact that the "axioms force themselves upon us asbeing true." This answers a question, untouched by Locke and Leibniz,why we choose one system, or set of axioms, and not another; that thechoice of a mathematical system is not arbitrary.

Gödel, in the "Supplement to the Second Edition" of "What is Cantor'sContinuum Problem?" remarked that a physical interpretation could notdecide open questions of set theory, i.e. there was (at the time ofhis writing {{and that did never change}}) no "physical set theory"although there is a physical geometry.